Representation of Part-Whole Relationships in SNOMED CT

Representation of Part-Whole Relationships in SNOMED CT A. Patrice Seyed 1, Alan Rector 2, Uli Sattler 2, Bijan Parsia 2, and Robert Stevens 2 1 Department of Computer Science and Engineering, University at Buffalo, USA 2 School of Computer Science, University of Manchester, UK ABSTRACT In this paper we investigate representation of the part-whole relationship in SNOMED CT. We discuss the current approach, based on SEP triples, and several translations of it, which involve DLs at different levels of expressivity. We intend that our analysis will concretely inform the SNOMED community about the important tradeoffs of expressivity for their ontology, and help with future decisions about the representation of the SNOMED CT s anatomical taxonomy. 1 INTRODUCTION A common pattern in knowledge representation is that a fault of a part is considered a fault of the whole. For example, a fault in the battery is a fault in the ignition system, and is a fault in the car. This pattern pervades common medical terminology: Heart disease includes diseases of any of the parts of the heart - muscle, valves, walls, etc. Gastrointestinal disease includes any disease of the stomach (gastrum) or any of the parts of the intestine. The same is true of procedures: fixing a heart valve is a kind of heart operation; repair of the retina is a kind of eye operation, etc. However, the pattern does not always hold. Amputation of the hand means amputation of the entire hand. Amputation of a finger is not a kind of Amputation of the hand (although it is a kind of Operation on hand ). Similarly, there are diseases that affect an entire organ, for example pancarditis means literally, inflammation throughout (pan) the heart. In general, therefore, there is a requirement to represent two cases: 1. Disorder/Procedure of A and/or any of its parts and 2. Disorder/Procedure of the entire A where A is any anatomical structure. In common medical language, the distinction is usually implicit. The distinction between the meaning of Operation on hand and Amputation of hand is left to the medical knowledge of the reader. It is only in unusual cases such as pancarditis ( inflammation throughout the heart ) that the distinction is made explicit in the language. However, when representing diseases and procedures formally, the distinction must be made explicitly and systematically. Over the past twenty years, there have been at least three mechanisms used to represent this pattern and the associated distinctions: 1.Propagation across transitive properties - the property used for of, usually has locus, is said to be inherited across the property part of. In modern description logics this is achieved by using property paths in subproperty axioms (Horrocks and Sattler, 2004). In earlier languages it was achieved by equivalent mechanisms known as right identities (Stearns et al., 2001) To whom correspondence should be addressed: apseyed@buffalo.edu or refined by (Rogers and Rector, 2000). This amounts to an axiom that the disorder of the part is a disorder of the whole. In this case a mechanism must be provided to cope with the exceptions when the rule does not apply. For example, in this case Heart disease is defined simply as Disorder that has locus some Heart. 2.Explicit definition of diseases as disjunctions - e.g., Heart disease is defined explicitly as Disease that has locus some Heart OR some part of Heart. 3.The use of Structure-Entity-Part (SEP) triples - separate classes for the whole or its parts (Structure), just the whole (Entity), or just the parts (Part). In this case Heart disease is defined as a Disorder that has locus some Heart Structure. Note that these three methods require different expressiveness in the description logic: 1.Propagation across transitive properties requires property-paths, which were not supported in early description logics and are not part of the basic specification of the standard starting description logic, ALC. They were originally thought to be intractable, but have since been shown not only to be tractable (Horrocks and Sattler, 2004) but to be even available in EL++, a maximal description logic with polynomial complexity (Baader et al., 2005). 2.Definition of diseases in terms of disjunctions requires a disjunction operator, which falls within ALC but outside EL++. It also requires transitive properties but not property paths. 3.SEP triples can be implemented within the simplest possible description logic, and does not require transitive properties, disjunction or properties paths (Hahn et al., 1999). The history of the use of these three methods and their variants is intertwined with the development of description logics for use with medical terminologies. The large description logic based terminology, SNOMED CT (Stearns et al., 2001) was originally developed using a variant of propagation along transitive properties (Method 1) as was GALEN, the other large description logic based terminology developed in the mid 1990s (Rector et al., 1997), (Rogers and Rector, 2000). SNOMED converted to Method 3, and is now being re-examined in the light of experience, one format being considered being a variant of Method 1 (Personal communication, Kent Spackman, 2011). Re-examination of these approaches is therefore particularly timely. The purpose of this paper is to explore variants on the three methods in the light of modern description logics, which has also been investigated in (Baader et al., 2009). Although we comment briefly on the apparent cognitive complexity for the user of the different representations, any of the three techniques might be hidden from users by syntactic and user interface mechanisms. 1

Seyed et al Our primary concern has been, therefore, with their formal, rather than cognitive aspects. 2 THE CURRENT APPROACH (SEP TRIPLES) We view SNOMED s set of class names C to be partitioned into: whole heart is a part of some body, and furthermore, a specific part of a myocardium or a whole myocardium is a part of some body. These axioms are also illustrated in Figure 2, and given formally below: C n C S C E C P where C S C E C P are specific to (human) anatomy. We use X S for class names in C S, X E for class names in C E, and X P for class names in C P. We assume that in any occurrence of X S, X E, or X P in an axiom, X refers to the same term, e.g., Heart. The SEP triple approach represents parthood implicitly within a class hierarchy (Hahn et al., 1999). For an anatomical entity of a certain kind, X S represents its Structure class, and refers to any part of the anatomical entity, including the entire entity. For instance, Heart S refers to any part of a heart or an entire heart. X E represents its Entire class, and refers to an entire anatomical entity, and X P represents its Part class, and refers to a certain part of an entity. For instance, Heart E refers to an entire heart, and Heart P refers to any part of a heart but not an entire heart. X E and X P classes are immediate subclasses of X S ; hence, Heart E and Heart P are immediate subclasses of Heart S. In the OWL version of the SNOMED CT ontology, 1 the SEP notation is part of the class label, for example Heart Structure, Entire Heart, and Part of Heart, but in this paper we apply subscripts for notational convenience. Ideally, a SEP triple is given for each anatomical entity, and every X S class (except that for the top anatomical class) is a subclass of some Y P class. 2 Fig. 2: Taxonomy of SEP Triple classes for Heart, Myocardium, and Body. Unlabeled arcs represent the subclass relationship. Myocardium E Myocardium S Heart P Heart S... Body P Body S Heart E Heart S... Body P Body S Fig. 1: Illustration of the Human Heart The heart has as part of it a muscular wall that contracts to pump blood out of the heart, and then relaxes as the heart refills with returning blood. This wall is called the myocardium. The heart and myocardium are illustrated in Figure 1. 3 Applying SEP triples, Myocardium S is a subclass of Heart P and Heart S is a subclass of Body P. This means that a specific part of a myocardium or a whole myocardium is a part of some heart, a specific part of a heart or a 1 http://www.nlm.nih.gov/research/umls/snomed/snomed main.html. 2 In SNOMED CT, however, the SEP triples are thus far incompletely populated. 3 http://texasheart.org/hic/topics/cond/myocard.cfm Note that, in SNOMED-CT, we neither find disjointness axioms for classes X E and X P nor covering axioms for X S, X E, and X P, although both are assumed to be true under the SEP triple theory. The SEP triples approach is iteratively applied along what is considered a partonomic hierarchy, for example for the anterior myocardium under the SEP triple for myocardium. The subsumption relationships are explicit, as given, but their reading is implicit; in particular, there is no part of property that links X E and X P. However, transitivity of the subsumption relation implies the transitivity of this implicit part of reading, and so transitive parthood entailments are determined by subsumption reasoning. We refer to the SEP triple approach from SNOMED- CT described so far and sketched in Figure 2 as the Current SEP Triple Approach (A). In the following sections we discuss several alternative approaches to representing part-whole relations and discuss their relative expressivity. On how approach A applies to subsumption reasoning for disorders, take for example a disorder specified in some anatomical location that is given as some class X S. Carditis is an inflammation that is located in some specific part of a heart, or a whole heart, 2

therefore Heart S. 4 These axioms and entailments are illustrated in Figure 3. 5 Fig. 4: No Entailment given the Part-Whole Relationship Fig. 3: Entailment given the Part-Whole Relationship. In the OWL representation class definition for Carditis, Inflammation is the range restriction for the property Associated morphology. We exclude this expression from the definition of Carditis above in order to simplify our examples. In SNOMED CT, there are numerous disorders defined in terms of their location. For instance, Myocarditis is inflammation that is located in some specific part of a myocardium or a whole myocardium, therefore, Myocardium S. As illustrated in Figure 3, because Myocardium S is a subclass of Heart S, the location for Myocarditis is also Heart S, and further, Myocarditis is a subclass of Carditis. We provide the DL representation for these findings and the corresponding inferences: Carditis Inflammation has locus.heart S Myocarditis Inflammation has locus.myocardium S Myocarditis Inflammation has locus.heart S Myocarditis Carditis A disorder that occurs at some location that is specified as a class X E, however, does not have such inferred subclasses. For example, Pancarditis is a disorder that is characterized by inflammation and is specified as being located in the entire heart and not just some part of the heart, therefore Heart E. Recall that Myocarditis is located in some specific part of the myocardium or the entire myocardium, therefore Myocardium S. As illustrated in Figure 4, it is accurately not entailed that Myocarditis is a subclass of Pancarditis: Pancarditis Inflammation has locus.heart E Myocarditis Inflammation has locus.myocarditis S Myocarditis Pancarditis 4 When there is any question, SNOMED CT uses the Structure class. 5 Inferred relationships are given as dotted arcs. 3 ALTERNATIVE APPROACHES FOR REPRESENTING PART-WHOLE RELATIONSHIPS We discuss five alternative approaches for representing part-whole relationships in SNOMED CT, the first of which is a reformulation of approach A. 3.1 Alternative Approach 1 We define Alternative Approach 1 (A 1 ) such that X S and X P are fully defined based on X E by introducing a transitive part of property, as described by Seidenberg and Rector (2006). SNOMED is the set-theoretic difference of the original anatomy-specific SNOMED CT axioms from all SNOMED CT axioms. We define A 1 as follows: SNOMED {X S X E part of.x E X S C S, X E C E } {X P part of.x E X P C P } Heart S and Heart P are therefore defined as follows: Heart S Heart E part of.heart E Heart P part of.heart E Myocardium S and Myocardium P are also defined in this manner, and the following axiom connects the two triples: Myocardium S Heart P Therefore Myocardium E and Myocardium P are subclasses of the expression part of.heart E. Because Myocarditis is an inflammation located in Myocardium S, and by inference Heart S, it appropriately follows that Myocarditis is a subclass of Carditis. 3.2 Alternative Approach 2 Alternative Approach 2 (A 2 ) is based on modifications to A 1 which is obtained by the following steps: 1.Remove all axioms of the form X E X S and X P X S. 3

Seyed et al 2.Replace all connecting axioms of the form X S Y P (where X and Y are different) with X part of.y. 3.Replace every occurrence of X S of a class name in C S with X part of.x and every occurrence of X E of a class name in C E with X. Applying step (2) in A 2, the connecting axiom for our running example classes is: Myocardium part of.heart Applying step (3) the example disorders are defined as: Carditis Inflammation has locus.(heart part of.heart) Myocarditis Inflammation has locus.(myocardium part of.myocardium) And by applying (3) to an inflammation disorder that is located in the entire heart, we apply the X class, Heart: Pancarditis Inflammation has locus.heart By the connecting axiom, every myocardium is a part of some heart, and because part of is transitive, every part of some myocardium is a part of some heart. Because Myocarditis is an inflammation of the myocardium or some part, both of which are parts of the heart, as in the prior two approaches, Myocarditis is a subclass of Carditis. 3.3 Alternative Approach 3 Alternative Approach 3 (A 3 ) repeats Step (1) from A 2, applies the proper part of property as a subproperty of part of, and includes the following steps for the connecting axiom and treatment of class names in C S and C E : 2.Replace all connecting axioms of the form X S Y P (where X and Y are different) with X proper part of.y. 3.Replace every occurrence of X S of a class name in C S with part of.x, and every occurrence of X E of a class name in C E with X. Additionally, for inferences of parthood: 4.Add proper part of part of. 5.Add part of proper part of proper part of. A 3 differs from A 2 in three important respects. First, for (3) part of.x replaces X part of.x; second, part of here is defined as reflexive, where it is assumed irreflexive in A 2 (and A 1 ); and third, Step (5) introduces a left identity axiom which is necessary because it allows us to infer: 6 part of.myocardium proper part of.heart and subsequently: Myocarditis has locus. proper part of.heart Applying (2) the connecting axiom for Myocardium and Heart is: Myocardium proper part of.heart But, different from A 2, applying (3) for our example disorders results in: Carditis Inflammation has locus. part of.heart Myocarditis Inflammation has locus. part of.myocardium The definition for Pancarditis remains the same as A 2. By the connecting axiom, along with (4) and the transitivity of part of, as was the case for A, A 1, and A 2, Myocarditis is an inferred subclass of Carditis. Note that by this approach, that (5) in connection with (4) leads to cycles (as described in (Baader et al., 2009)), which is not allowed in the DL language that underlies OWL 2. Fortunately this does not pose any problems for those reasoners implemented for EL++ expressivity. 3.4 Alternative Approach 4 Alternative Approach 4 (A 4 ) introduces the has locus entire property, a subproperty of has locus, which expresses when a finding is located in some X E class. This approach was first introduced in (Baader et al., 2009)). A 4 repeats Step (1) from A 2, as A 3 did, and repeats Step (2), from A 3, while including the following step for the treatment of class names in C S and C E : 7 3.Replace every occurrence of X S of a class name in C S with X and every occurrence of has locus.x E of a class name in C E with has locus entire.x. A 4 also repeats (4) and (5) from A 3, while including an additional step: 6.Add has locus part of has locus. A 4 differs from A 3 in two respects. First, in (3) A 4 treats X instead of part of.x as a replacement for X S, and employs the has locus entire property. Second, for A 4 in (6) a right identity axiom is applied, where the has locus property is transitive over the part of relation. Applying (2) the connecting axiom for Myocardium and Heart is the same as for A 3. Different from all other alternative approaches, applying (3) for our example disorders results in: Carditis Inflammation has locus.heart Myocarditis Inflammation has locus.myocardium Also applying (3) to an inflammation disorder that is located in the entire heart yields: Pancarditis Inflammation has locus entire.heart which prevents erroneous propagation via the right identity axiom. By the connecting axiom, along with (4) and (5), the same inferences hold for our example disorders, primarily that Myocarditis is a subclass of Carditis. 4 DISCUSSION In Section 1 we introduced three major methods for representing part-whole relationships, by applying: (1) transitive properties (2) 6 A left identity axiom can be formalized in OWL2 as a property chain axiom. 7 Baader et al. (2009) also keep Structure and Part expressions fully defined as X S part of.x and X P propert part of.x, for legacy reasons. 4

disjunctions and (3) SEP triples. In Section 2 we introduced the logic underlying the current approach in SNOMED CT, and in Section 3 the logic underlying four alternative approaches. The approach used in SNOMED CT currently, A, is an application of (3), which is within ALC expressivity. A 1 is an application of both (2) and (3), while A 2 is an application of just (2); both are within ALC but are outside EL++ due to disjunctions. A 3 and A 4 are an application of just (1), and fall within EL++. In general, there is a modeling choice between treating a generalized part of property as reflexive or irreflexive. In A 1 and A 2 the part of property corresponds to the latter choice, and is assumed irreflexive. It is only assumed because in OWL2 we cannot assert that a transitive property is irreflexive, but we can assert that a transitive property is reflexive. Therefore we can also introduce approaches (as shown for A 3 and A 4 ) which correspond to the former choice, where part of is reflexive, which can be therefore be applied directly and without disjunctions for representing the X S class expression. In these approaches a subproperty proper of, again assumed irreflexive, is also introduced for representing the X P class expression; subsequently cyclic role chains are required in order for the respective ontologies to entail correct subclasses of the pattern proper part.x. Also, an important distinction between the approaches A 3 and A 4 is that while A 4 has the same approach as A 3 for translating and thus representing SEP class expressions (via patterns part of.x and propert part of.x for Structure and Part expressions, respectively), A 4 has a different approach for inheritance of properties along a partonomy. For A 4 the inheritance is through a right identity axiom, while for A 3 it is through the transitivity of part of. 5 CONCLUSION A major difference between the current approach, A, and the alternative approaches, A 1 - A 4, is that the former offers only a propositional representation and the latter offer a relational representation of parthood. A does not model partonomic structure, but rather partonomic level. By modeling partonomic structure explicitly via the part of property we can make explicit statements of how part of interacts with other properties (i.e., laterality): haslat.left ( part of.( haslat. haslat.left)) says that, if something has a left laterality, then, what it is a part of, if this whole has a laterality at all, it has a left laterality. Modelling this kind of interaction requires an explicit part of - which then can, of course, be used in sub-role and inverse role axioms as well. It is reported by users of SNOMED-specific browsers that SEP triples are cumbersome to browse and search through. We suggest that this problem can be addressed by providing more intuitive labels. In the context of user navigation, it is simply a rendering issue. It is for this reason we do not necessarily recommend against the A or A 1 approach. Nevertheless, A 1 - A 4 do provide the benefit of allowing a user to explicitly query parts, for A queries require knowledge of the SEP class hierarchy. In preliminary performance testing, A 1 performed the worst for classification across all the DL reasoners we tested. This is no doubt attributable to the inclusion of disjuncts in the class definitions, and corresponding unfolding performed by the reasoner. Despite this, A 1 has utility as a representation used for mapping between ontologies that use the propositional approach and those that use the relational approach. Clearly, formulations that include the part of property facilitate ontology modularity, merging, and enrichment where A 1 can serve as a bridge. In future work we will empirically measure classification and query performance for these different SNOMED ontology formulations approaches across several DL reasoners. Furthermore, we will apply an evaluation framework across the formulations for various types of information requests. In that work we will address what kinds of information requests are expressible as OWL class expressions, and which require a more expressive query language. ACKNOWLEDGEMENTS This work was supported by the National Science Foundation (NSF Grant IIS-1107011) in conjunction with IJCAI 2011. We would like to give thanks to Luigi Iannone for assistance in using the OPPL scripting toolkit and useful advice for using the OWLAPI for the translation work. We would also like to give thanks to Kent Spackman and the reviewers for their helpful feedback. 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